book-recommendations

[vital bane]

my condolences

I mean it's a good book, but it's just so old

wth that's crazy! Emil Artin or Michael Artin?

[cunning elk]

uh

lemme check

michael

[vital bane]

that's pretty cool

[cunning elk]

https://www.mathgenealogy.org/id.php?id=13041

[vernal pewter]

surely the hardest part about getting your piece of paper in the US is paying for school fees

[vital bane]

Unless you get a scholarship

[cunning elk]

how scarce are those for grad

the big scholarship I have for undergrad is being significantly cut for newly admitted students receiving that same scholarship

[vital bane]

for grad? If you're doing a PhD don't you get a stipend?

[vital bane]

[cunning elk]

for say masters’

hopefully id be applying to fully funded PhD programs

[vital bane]

In the US? I think that's rare since most people just do a PhD

[cunning elk]

epic

time to get zero (0) offers next year 😭

[full cairn]

Not sure, but doesn't seem like it

[upper estuary]

hi friends!! This has probably been asked a thousand times here but what textbook would you recommend for self-learning Discrete math?

[upper estuary]

Rosen and Epp seem to be the two most common recommendations, but I'm not sure which one to pick

[snow halo]

Flip a coin

[upper estuary]

💀

honestly i might just do that

I don't know if I have one, the world b cashless these days

[vital bane]

You can flip a coin online

just google "coin flip"

[vernal pewter]

just read a fixed number of bytes from /dev/urandom and see if the bit of your choice is 1 or 0

[remote vortex]

Flip a credit card

[dapper root]

Lol

[grand thistle]

ur right fuck 3.6

[raven cloak]

What is the book you guys would recommend that is about arithmetic

And 2d,3d geometry if possible

[foggy heart]

Hi folks! I am looking for a chill read on linear programming/combinatorial optimization. I don't have any time for proofs as I'm in industry but I want to get a good intuition. Do you have any recommendations?

[versed kettle]

hey. anyone got specific sources like books or pdf data for integral calculus. i want to improve my integral skills but cant really find specific material to do so. like commonly known books or something with as many exercises as possible. :3

[graceful moon]

Stewart’s calculus will have more basic integration problems than anyone could need in a lifetime

[junior elk]

And if you want harder questions you have the hot problems

[wraith cave]

why not try the 100 integrals from bprp yourself

[warm nova]

Mathematics R D sharma is pretty good

[versed kettle]

i dont really know if that is what you mean. but i've found an about 1300 page long pdf data of a book called CALCULUS EARLY TRANSCENDENTALS SIXTH EDITION by JAMES STEWART
at least what i found out. that book covers a lot of problems. i just wondered a bit bc if i want to buy this monster it would almost cost me a kidney. so idk xd. but if it was what you meant ty :>

[graceful moon]

That is the book I’m referring to. There’s loads of copies available online and you should be able to find a used copy for a good price if you really want a physical edition, it’s pretty much the de facto calculus textbook in most of the English speaking world

[versed kettle]

thanks a lot :P

[cunning elk]

the “hard problems” in that book aren’t that hard

[versed kettle]

"hard problems"? at the end of every chapter there are "problems plus". those?

if they are the so called "hard problems" and they were exactly those in which ive looked then.... well. i better "keep" them for later. might be better for my own safety qwq

[lyric storm]

Hi, I'm trying to read spin geometry by lawson and was wondering if there are any resources on rep theory, to make the reading go smoother? I basically have no formal knowledge in rep theory.

[cursive rivet]

Fulton and Harris' book has everything you need iirc (especially the second part on Lie groups)

[slate pilot]

How do u guys read math books? Math is awesome, but doesn’t it get mad tiring reading entire books?

[vernal pewter]

1. You might not read the whole book, 2) Even if you do end up reading the whole book (and doing the exercises, very important!) it might be in 100 sittings so each individual sitting is the right level of tiring

[dim pendant]

You should also just not read the whole book unless you know you either should, or that it will all be relevant

[still panther]

you should read the whole book because knowing useless facts is fun

[dim pendant]

For example, Munkres's Topology. Half of it is algebraic topology, so if you're, for example, looking to study functional analysis, then you only need the first half

And that's probably overkill if you take good real and complex analysis courses

Basic metric topology is enough

[still panther]

i mean tbh ive gotten a lot of mileage out of reading shit i thought was entirely useless

its not a good strategy if you have a concrete goal in mind and you need to work towards it

[dim pendant]

It's fine to read the entire book, but at an advanced level (e.g. working through a masters degree), you'll never get anywhere.

[still panther]

yeah it should be treated as a recreational activity

[mossy flume]

^^

[dim pendant]

I guess but if I'm studying math to be a mathematician, then I will dedicate my math time to math I think I need, or really enjoy

[mossy flume]

only times I've worked through large chunks of textbooks are as self study or I was explicitly doing a reading course

[dim pendant]

Every minute you spend doing something else is a minute further away you become from your bigger goals

[mossy flume]

I do think trying to do this for at least a couple hours a week is important to avoid burnout, especially if you're only doing courses in material you don't really enjoy (as was the case for me last semester)

[rigid trail]

i sometime s"flip through" math books like a normal book recreationally, but to actually learn i will do the exercises and carefully follow all theorem/lemma/etc proofs

[still panther]

thats a recipe to crash and burn after a certain amount of time

[mossy flume]

^^^^

[dim pendant]

Not if you just enjoy the math you want to do lol

It wouldn't be a goal of mine if I didn't love it

[mossy flume]

ok but math is hard work on the mind

like you can enjoy the hard work but that doesn't change the fact that it's taxing

[dim pendant]

And it gets even harder when you do extra work that has nothing to do with your primary motivation

[mossy flume]

you can enjoy lifting weights but you can't lift without taking rest

same with any studies, your brain needs rest

and a significant amount of it

your brain works better with rest

so you likely can get more done if you actually take breaks and have hobbies outside of work

since then when you do work, you'll be in a better spot mentally

[dim pendant]

I never said you need to do math all the time. I said that if you have professional goals, you should put as much of your math time as you can into working towards that goal, not doing aribtary math

[rigid trail]

sometimes i enjoy writing whatever proofs for my homework and i don't feel like stopping while being on a roll, but by the third hour i begin hallucinating blatantly incorrect facts or reasoning and my brain starts to make connections that are just wrong

thats when i stop lmao

[still panther]

unfortunately im built the same

[rigid trail]

usually before but that happens when i really like my work

[still panther]

a misstep on my part

[dim pendant]

Yeye. I know a theoretical physicist and he says that he doesn't get more than about 4 hours of work done per day lol

The brain can only do so much hard work

[rigid trail]

im no teven joking when i say that once i convinced myself that ALL subsequences of a sequence in a compact space converge 💀

late night math work goes crazy

[slate pilot]

I’m not, lol. That’s why I ask

[rough umbra]

If I wanted to teach myself a complex analysis course covering

Analytic functions, Cauchy-Riemann equations, Goursat's theorem, Cauchy's theorems, Morera's theorem, Liouville's theorem, maximum modulus principle, harmonic functions, Schwarz's lemma, isolated singularities, Laurent series, residue theorem.
sections 1-3 of Freitag and Busam would be all of this right?

[naive lava]

not exactly sure about harmonic functions, but others are covered here or can be proven with things listed here

[dim pendant]

Are you familiar with the content? Also, how much experience do you have with math? Your answers to these questions will help provide you with more specific advice.

[slate pilot]

What content? And calc BC, calc 3D, linear algebra, differential equations, and lagrangian mechanics

[dim pendant]

Of the book you're considering self studying

[slate pilot]

Ah, I misunderstood, I’m not considering any book

[dim pendant]

Oh you just straight up asked how we do it

[slate pilot]

Yuh

[dim pendant]

We don't want to read math books

We're just obsessed with math so it follows that we have to

Kind of like how you grind out any other skill you want to master

[slate pilot]

So it’s a means to an end

[dim pendant]

Yeah, eventually it becomes somewhat fun but it can be fun with the proper attitude, and the help of a good author

Some math books are genuinely a blast to read, and others are dry

[slate pilot]

What would the proper attitude? One that commands respect with how wonderfully insightful and brilliant they are, or one that incorporates humor and clever connections and analogies?

[dim pendant]

Perhaps all you need to begin is a sense of excitement or anticipation that the work will pay off

Each concept, exercise, moment of confusion is one step towards your goal

So you might as well make the most

[slate pilot]

Ohh, I thought u mean the attitude of the author

What got you interested in math in the first place? For me, I think it started with a 3Blue1brown video

With his beautiful animations, lovely and calm asmr voice, and very amazing teaching skills

[dim pendant]

It was physics. I kid you not, as a dumb 8th grader I saw some sophisticated physics equation and I had some friend in college and he told me that if I wanted to understand it, I would need to learn calculus

So at the end of 8th grade I speedran algebra and studied Calc and trig at the same time. Then I joined a math community online and started learning topology, category theory, and ring/field theory after a quick exposition to set theory and proofs

And I just kinda never looked back

I guess I was one of those kids who should've been a prodigy but slacked off too much lol

[drowsy nacelle]

aren’t we all, man

[trail hemlock]

"i could have been pope but i decided to pursue master studies" ahh

[drowsy nacelle]

LMAO

[dim pendant]

Yeah I made the mistake of studying differential equations and the integrals were so boring that I burned out and just played video games for the next 4 years

Learned basically a semester's worth of math in that time

[manic cairn]

also my route

i thought i wanted to do physics, but then encountered euler-lagrange as a “proof” that lines were the shortest distance between two points, and fourier transforms in general

picked up grafakos classical fourier analysis

completely incomprehensible. it begins by recalling a bunch of measure theory

then i found lang’s undergrad books and later munkres and lang’s algebra

fell in love with algebra

wasted 4 years of my life depressed and addicted to video games

and here we are

[dim pendant]

Lmfaoo twins

Fourier and harmonic analysis are constant reminders to me that I'm consciously choosing to not engage with incredibly interesting math

[half void]

Omfg i just got a copy of each of Bourbaki’s algebra in french from my advisor

I’m so excited to read it

[remote sparrow]

https://a.co/d/2B4ybEh

crazy amazon recommendation

💀

@halcyon mesa

[gray jungle]

The ai slop thickens

[rigid trail]

Whole ass series 😭

[normal crystal]

she even includes python examples in some of the books
ai girl boss

WHAT IF THIS IS HER/HIM
https://www.linkedin.com/in/awesome-sky

[remote sparrow]

😭

[normal crystal]

the real plot twist would be if it's Math Sorcerer again
you know citytutoringmath is just hoping so, ready to pounce

I would love if Marh Sorcerer found a clip of citytutoringmath without his anachronistic cosplay
it's out there, do your thing internets

[raven cloak]

Zamn 🔥

Btw why is the book cover a portrait of a korean

[cunning elk]

null

this so much

one of my gen ed professors first year required us to print out all our readings

i now see why she did that

you'd still be reading off a screen which is the main issue no?

or check them out from your university library ig

[vital bane]

huh?

[remote sparrow]

i am

[vital bane]

I don't use sticky notes but I do write with a pencil in my books

sometimes

when it is required

be wealthy
buy the springer company
profit (loss)

But at least you'll get all the books

You said "Your textbooks" so I'd assume personal

[fresh skiff]

math book with a girl on cover

[cunning elk]

live service games but for textbooks!!!!!!!!!

oh for one of my freshman music classes

we had to “buy” an ear skills “ebook”

that was nothing but a buncha blank sheet music and shitty MIDI generated audio files

the cost?

$90

😭

i was like “I ain’t paying for that shit”

downloaded the files I needed and immediately refunded

[remote vortex]

Think bigger: gacha

You pull problems and hints from banners.

[tribal crow]

[heady ember]

You don't use sticky notes to cover up the hints?

[fast jetty]

Source?

[molten gulch]

<@&268886789983436800> inappropriate

[naive lava]

^ this

I usually write clarifications and stuff so the next person that reads doesn't have to go trough the same pain as I did

[trail hemlock]

has the math sorcerer gone too far

[grand thistle]

hi blackbeard

[merry sphinx]

what da hail

youre one of those...

[vital bane]

Yeah 🗿

[vital bane]

Real social service

But I don't do these on library books (I kind of do but not to the extent I do with my own books)

[vital bane]

Amazon Rainforest

[vital bane]

I read the hints

[heady ember]

...

[vital bane]

When I'm going to prove a statement which was already proven in the book, I use my hand to cover up the proof in the book

and simply commit the statement to memory and I close the book

[rigid trail]

Pencil??

oh in the books

[indigo notch]

Those seem legit.

Tablet?

[dim pendant]

Ai or not, I always find it so funny when some completely random person goes "Yeah, I'm me so people would love to read my book spam." and then they publish a bunch of useless content

[molten gulch]

Absolutely

The book must never be bent, creased, anything, if it cannot close properly, it must be set immediately, etc...

[dim pendant]

I was the type, and then I realized that it's not all that serious. If the book is not of use to you, "use it in some other way" (borrowing exists, for example), and if the book is of use to the you, simply don't mistreat it. So long as the book can be read and isn't [prematurely] falling apart, it's fine.

At the end of the day, anything could happen to a book. Your house could burn down, your shelf could fall apart, a pet could rip it up, etc. No point in having anxiety about the condition of a book I don't keep at an arm's length

[indigo notch]

I never wrote in them or highlighted in them, but I never cared too much about keeping them in pristine condition. These books are meant to be used to me.

[indigo notch]

Sometimes, a book falling apart can be a point of pride. Some religious people have this attitude toward their scriptures, as it's a sign that they're being read.

And I figure if the worst does happen to a book, I can likely replace it. I don't have anything rare.

True, math textbooks tend to be expensive. That's why I'm a huge fan of Schaum's and Dover. 😉

[half void]

I try but i cant…

They get damaged in my backpack

[signal mountain]

books are meant to be used imo

better a much loved much worn book than a pristine book thats unused

[naive lava]

depends

If it's something I'm not planning to use as a reference

then I don't really mind what happenes to it

but if it is, I'll be more careful with it

[trail hemlock]

hi

[normal crystal]

If I order an old book from a seller who last had a seller review in 2017
what's the chance he💀

[rigid trail]

no

[rigid trail]

well you just have to know that i dont have my books in pristine condition

[grim ore]

I try to keep them nice enough, but idk wear and tear esp for paperbacks is hard

Hardcovers are a little easier, but chances are the corners of the cover gets roughed up

[dim pendant]

Yeah I much prefer to memorize the page number I leave off on, keep my hands clean when I use them, and not shove them somewhere so the pages get bent up and whatnot

But one of my first real undergraduate math books I was given, my mom spilled wine on it on our flight to Alaska

Taught me real quick that I'll just have to let perfection go lol

Actually both of my first real math books lol

[rigid trail]

i scribble in my textbooks

immediately the spell of wanting to keep everything perfect is broken

it's so great

i can now throw things in my backpack

[dim pendant]

I wish I could scribble in my textbooks but I can't hear my reasoning thoughts, so the only things I think to write down are notes, proofs, and exercise work

[grim ore]

tbf, I rarely do this too

But I moreso stick to journals

I stickynote pages that I want to look back at if anything and index a page in my journal lol

[rigid trail]

i fold corners

i want my books to feel used 🗣️

battle scars from my study

[dim pendant]

The first book I was ever given had pages falling out and writing all over so it overall left a bad impression in my mouth for used books

But once you get past your basic undergrad classes you don't get to buy cheap. Used it is.

[rigid trail]

yeah dude i cannot afford brand new stuff lmao

[remote vortex]

I write wild conjectures in the margins, claiming I have extraordinary proofs that don't fit into the space

[rigid trail]

but the brand new ones gifted to me, i still write in them

[dim pendant]

I wish I got gifted math books 😭

All book sellers should agree to sell Serre for under $50 before tax

[rigid trail]

i just ask family members to get me textbooks for holidays or my birthday, instead of getting whatever presents that i wouldnt care about anyway

sometimes they get me new textbooks for some reason but i wont complain

[dim pendant]

Twins I did too but now I'm a grown ass man 💀

[grim ore]

Honestly, Ive gotten to a point where for birthdays, Id just ask for like a 20-40 dollar textbook and thats good enough, but otherwise id be paying out of pocket most of the time

[rigid trail]

you still can ask prob

[dim pendant]

Nah cuz the only book I want is Neukirch 💔

[grim ore]

Yeah these are gifts that my friends bring, i insist rather than a wine or champagne bottle lol

[dim pendant]

Gotta buy that one myself

[rigid trail]

hard to get textbooks that cheap 😔

depends on family dynamics maybe

[grim ore]

They run sales pretty often and I only ask for textbooks from a curated list ofc lol

I wouldnt want people to spend more than 60 max

[rigid trail]

nice

[grim ore]

Also some retailers have discounts/coupons that make it cheaper, for example Amazon sells springer texts cheaper most of the time

Lets move to #math-discussion ?

I didnt realize we were in books

[remote sparrow]

https://tenor.com/view/mods-push-back-his-hairline-gif-11241907652566626707

[molten gulch]

Our mum does this, it drives us positively mad

[naive lava]

your mom folds corners of your math textbooks?

[dim pendant]

I think there are always regional limitations but the word around the street is that you can pay small companies to print books, so if you send in a PDF and format the exterior pages, you can get "any book you want" for a reasonably reduced price

[dim pendant]

The evil mom, who comes into my room, bends pages in my math books, and goes about her daily business

[dim pendant]

One of my Scandinavian buddies was doing it and spending only about $35 for books that would've been far more

[runic karma]

Does anyone know of any books purely on methods of solving integrals?

If those are even a thing

Like a book on more uncommon methods of solving them

[dim pendant]

Try asking chatgpt. I don't know of any but it may be fruitful to search something along the lines of "mit integration bee primer"

[naive lava]

gimme a sec i got something for you

[cunning elk]

!nogpt

[hybrid sparrow]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[dim pendant]

Chatgpt is just a better Google search

[naive lava]

https://link.springer.com/book/10.1007/978-3-031-24228-1

[indigo notch]

I have Elsevier taste on a Schaum's budget.

[runic karma]

Oh interesting, I'll have to take a look

Preciate the recommendation

[naive lava]

also, https://www.wolfram.com/mathematica/

[dim pendant]

@runic karma could you open your dms or whatever, I've got a link for you that im not allowed to send in this server for copyright reasons

[runic karma]

Gotcha

[dim pendant]

That guy is about to be an integration pro

[runic karma]

LOL I'm looking for analytic solutions to a weird integral so I won't be needing this

I am an https://www.integral-calculator.com/ enjoyer tho

[remote sparrow]

https://a.co/d/eejfety

[naive lava]

uhh

mathematica does that

[runic karma]

I don't think it'll do this one

[naive lava]

also https://dlmf.nist.gov/

if you can't find ur integral here

or mathematica can't do it

you probably can't do the integral yourself

so i wouldn't bother with it tbh

[runic karma]

there is a decent chance it can't be done tbh

the integral is sin^2(1/(x(2-x))

is of the function*

chances of solving are indeed grim but worst case scenario I get better at doing regular integrals while trying to solve this one

so it's a win-win scenario

[cunning elk]

"better google search" is fucking WILD 😭

you can't be serious

please don't tell me you actually drank the gpt kool aid

[dim pendant]

It is trained on a large set of data. Anything that is commonly discussed online will be pretty well handled by gpt

It is simply bad at niche details that are not clear

[cunning elk]

it has no idea what it's actually saying

[dim pendant]

That doesn't mean it's always wrong

[cunning elk]

it just says "hmm probabilistically what's the most likely next word"

it's wrong unacceptably often.

all because people can't be arsed to USE THEIR OWN FUCKING BRAINS

[dim pendant]

It will not give you bad answers if you ask "what are some good books to learn advanced integration techniques beyond what is found in standard calculus"

[cunning elk]

it will hallucinate texts/articles that DO NOT EXIST

what about this makes you think it's a "better google search"

[dim pendant]

It hallucinate some things \neq it hallucinates common information

[cunning elk]

even that's not a guarantee

[dim pendant]

The newer models even source their information directly from Google searches

[cunning elk]

and i am fundamentally opposed to gpt usage on principle

[dim pendant]

You're opposed to the use of it at all

[cunning elk]

that are also filled with ai slop

[dim pendant]

Which is a very naive opinion

[cunning elk]

ai bro detected opinion discarded

[dim pendant]

Insane how some people call themselves open minded and then generalize things like this

[naive lava]

I think it perfoms okay on wide topics but starts to fail miserably on nieche stuff

also, veryfiying some info is usually faster than finding it

so if you can't find it, it's okay ig

[cunning elk]

and what results does it pull up?

that's right, the same SEO'd ai slop nonsense that's at the top of search results

[naive lava]

idk if i ask where can i find proof of this theorem, it'll gimme a few books and that gives me a place to start looking

[dim pendant]

I just asked chatgpt for a gentle introduction to complex analysis for undergrads and it gave me an answer that was higher quality than any single response you'd get on this server (which I know is correct because I know all of the books it recommended)

Took me 10 seconds to ask

It would tell you Pinter

And I would agree, Pinter is great especially for its exercises (which it would also emphasize if asked)

Pinter doesn't even assume you know what a function of sets is

Lol

You're good, I'd engage but I am at work so I gotta dip

[valid narwhal]

just use closed form equation for the fibonacci numbers

dont really need a program

[limber bolt]

I am taking lin alg this semester and my prof told me the one I am taking is far more proof based. I don't have much experience with proof based courses so I am wondering what text I should read that has a gentle introduction to linear algebra yet has abstract depth

is Jean Dieudonne's lin alg and geometry a good one?

[molten gulch]

She folds the corners of all of her books. Luckily, she never touches ours.

[dim pendant]

Before the course starts, I would find a book on real analysis or general topology that talks about proofs in the first chapter and just study that first chapter

Then you can practice applying the proofs with a gentle book like "linear algebra done right"

Though I think in the first chapter, the exercises aren't well thought out

The hardest part about writing proofs is writing any specific proof, not the proof process. You intuitively understand what it means to prove something already.

One such book I can think of is "An introduction to real analysis" by Schramm. He has a sufficiently well done first chapter on writing proofs. Another option I believe is Munkres topology.

Much more brief but for some people it's a good enough start

[limber bolt]

just to be clear, analysis is not a prereq to lin alg right? are you suggesting it to boost my mathematical maturity

[dim pendant]

Cktrect

I'm suggesting it because a proofs book is too long

So you should make quick work of it

I mean unless you like taking your time then you could do an entire proofs book

[limber bolt]

i see, that makes sense

i wanted to get into a computational lin alg course but the slots were full

[dim pendant]

Understandable. If you're looking to go down the pure math road, you'll get a lot out of the pure linear algebra course, otherwise sorry for your loss

Maybe you'll convert but obviously if you're an engineer or a physicist you probably just wanna learn the computations and get out

[cunning elk]

to learn the basics of linalg you don't need analysis lol

[normal crystal]

insising convinced me
maybe he is an LLM

[dim pendant]

Yeah just to triple clarify, I'm saying to pick an analysis book with a decent chapter on proofs, and then to study that one chapter

[remote sparrow]

#book-recommendations message

[dim pendant]

Yeah, draw the line at doing math. You can ask it to help find you non-professional resources, but its limit is roughly calculus and some competition math, though I don't trust it to do anything beyond easy calculations

[heady ember]

Linear Algebra by Friedberg, Insel, and Spence.

Its a gentle proof-based linear algebra book; you can use it as an intro to proofs, too.

[cunning elk]

FIS is a classic yea

[dim pendant]

I hear a lot of split 50/50 reviews on that one, specifically on the exercises

I also hear that most people who approach the book don't feel that it is gentle

Anyone reading any interesting books lately? I was browsing YouTube aimlessly and came across a book published in 2024 that teaches abstract algebra behind the motivation of Galois theory all the way through. I've been exploring it to see if I can learn anything new.

It's called "Abstract Algebra" by Marco Hien

[dim pendant]

It is very gentle in its methodology but that isn't really an introduction haha it's an overview

Still an incredible book for any mathematician though

[vital bane]

You can use it as an introduction if you are familiar with some pure math

like analysis

[dim pendant]

Yeah true

I have a buddy who used it and then returned to algebra with Aluffi. Bro is goated now

[vital bane]

tbh you don't even need to have gone through another field of math, I think all you need is to have read an "intro to proofs" book

Yes

it starts at the very basics

There's like 6 whole chapters of just group theory and 3 chapters of ring theory

Then vector spaces and modules then field and galois theory then you have stuff like some commutative algebra and representation theory

[dim pendant]

In my opinion abstract algebra is the best undergraduate course for a student with only a proofs course and calculus under their belts. I mean if it were up to me you'd do linear algebra with Calc 2 so that you see it before Calc 3, and then do linear algebra properly after you know what a field is

[vital bane]

Nope because that's not abstract algebra

[dim pendant]

Your first semester of rigorous math should totally be algebra and real analysis

[vital bane]

I think that's how it is in most places no?

[native cradle]

can I have book reccs for CA for someone who has done bartle and sherbert

asking for someone I know

[dim pendant]

Nah I think most people get real analysis and they see algebra within one or two consecutive semesters

I'm speaking as a north American btw

[vital bane]

#book-recommendations message

[cunning elk]

classic "is y=mx+b linear algebra 🤓"

[dim pendant]

In Europe you've done group theory and a first course in analysis by the end of year one

[cunning elk]

😭

[dim pendant]

Don't make fun of them for not knowing better lol

[vital bane]

tbh it technically is linear algebra if b = 0 it's a vector subspace if b \neq 0 then it's an affine subspace

[trail hemlock]

you and grass write similarly

hmm

[limber bolt]

there is NO way my prof recommended me this text

i think i am cooked for lin alg

[trail hemlock]

what text is this

[dim pendant]

That book looks old as hell

[limber bolt]

this one

[trail hemlock]

lol the formatting is evil.

[limber bolt]

it just keeps on introducing properties and axioms and stuff and stuff

[dim pendant]

Tell bro to install the latest linear algebra updates

[native cradle]

thanks

Use LADR

[dim pendant]

This is what pure math feels like until you take your first distinctly graduate courses haha

[vital bane]

LADR?!?!?

[native cradle]

I loved it

[limber bolt]

im an engineering major 😭

i should not be going through this

[vital bane]

I like Gilbert Strang would be suitable for you

[vital bane]

I didn't like it

[limber bolt]

it is a proof based course

[vital bane]

Then FIS

[native cradle]

then LADR / FIS

[limber bolt]

im trying out axlers

[native cradle]

I have both, I prefer LADR, though FIS is nice too

[limber bolt]

it seems gentle

[native cradle]

use the 4th edition btw, it's free :D

[cunning elk]

strang is too incoherent for my tastes

[limber bolt]

i will obtain the physical copy from the library

[native cradle]

It's quite rigrous though

[cunning elk]

watched a few of his OCW lectures to see what the big deal was

and there's no rhyme or reason to how he structures them

[limber bolt]

i think his deal is that engineering students love him

[cunning elk]

nonetheless his RMP is filled with glazers whose eyes pop out of their sockets as soon as they see the word "MIT"

[dim pendant]

If you come from a pure math background I don't find this surprising

Computational linear algebra is just matrix hell there's no beauty to it

It's just a bundle of trash

[cunning elk]

true and real

the linalg class i took first year of undergrad was actual dogshit

both in the amount of matrix spam there was

and the utter lack of substantial content covered

no jordan forms, LU decompositions, etc

we fucking stopped at basic eigenvalues/diagonalization 😭

[rain hound]

Linear Algebra Done Wrong by Treil is good and probably more suitable for engineers.

[dim pendant]

this is what breaks mfs 😭

[rain hound]

Axler is good but, probably better off as a second course (if needed)

Unless one is a pure mathematician or wanting to do theoretical physics

[dim pendant]

oh true you do need to know your vector spaces to be a modern theoretical physicist

shoutout to all my Hilbert spaces out there

[vital bane]

even as an old school theoretical physicist

[dim pendant]

true, anything from and beyond basic Qm right

[vital bane]

hilbert spaces were introduced to physics more than a 100 years ago

[limber bolt]

a vector space is a free and open space for vectors to talk about their problems

[dim pendant]

down with them!

[dim pendant]

my favorite spaces are open, though

"so all of them" shut up

[rain hound]

Yeah Axler is just better at pedagogy than most mathematicians lol.

[vital bane]

I didn't really notice that tbh

[dim pendant]

I second not noticing it

[vital bane]

In the sense that the exposition in Axler was good, alright

[dim pendant]

Well no it's clear in his book on integration

[vital bane]

but not "better than most mathematicians"

[limber bolt]

i mean axler has a cat

[vital bane]

or maybe you mean better than most research mathematicians and not better than most book authors

[naive lava]

well

[vital bane]

in which case I don't think that's saying much

[naive lava]

all post 17th century physcists must know at least a bit of LA

[rain hound]

Even for book authors I’d say it tbh. I really enjoyed both his LA and analysis books.

[dim pendant]

oh, neat. tell me you don't study physics without saying it 😉

[naive lava]

uhm actually

[vital bane]

I haven't tried his measure theory book but I have heard mostly good things about it

[dim pendant]

(I had topological spaces in mind, to be transparent)

[rain hound]

Yeah it shines a bit better here. There’s more good books on linear algebra than (graduate) analysis.

imo

[vital bane]

he is literally doing a PhD in physics

[dim pendant]

I meant me XD

Wasn't really clear but yeah I clearly don't study physics

[naive lava]

don't be so sure lmao

[dim pendant]

Fair. In my opinion his method is so.. sound, that his analysis is actually boring to read

[vital bane]

topological vector spaces?

[dim pendant]

yeah I guess XD

[naive lava]

even than

[vital bane]

yeah

[naive lava]

closed subspaces are much more beautiful

first of all

riesz's lemma

my beloved

[vital bane]

if you go to infinite dimensions I think by default you work with TVS

since convergence of Schauder basis

[dim pendant]

Woah woah woah, who was it who said that mathematicians generally prefer open sets?

Let's keep it this way...

[naive lava]

uhh

there are infinite dimensional normed spaces too

[vital bane]

True true

[naive lava]

doesn't always exists

sad day in math

[vital bane]

that's also true

truly sad

Gilbert Strang

or you could do FIS as well

[dim pendant]

yes, I will sit here and pretend I know anything about infinite-dimensional vector spaces

[naive lava]

backside of griffisth QM

then read shankar

[dim pendant]

be a chad. skip intro linear algebra and pick it up in a big fat algebra book (Lang, Dummit, etc.)

[vital bane]

Tbh Shankar's first chapter is pretty good

I love his explanation of Gram-Schmidt

[naive lava]

just skip srtaight to lang's algebra

[dim pendant]

LOOOL

[vital bane]

Which was MUCH better than the explanation in Axler's LADR 3rd ed. btw

[naive lava]

I loved the basis decomposition part

[dim pendant]

yeah, I meant that it was a big fat algebra book.. if you don't know any lin alg, Lang is probably too hard... probably

[vital bane]

more than being "hard" it's about lacking prerequisites

[naive lava]

you can see how ppl actually solve problems in QM in CM

[dim pendant]

Lang would probably be perfect if he didn't leave all of his exercises to the end of the freaking chapter

[naive lava]

It has a appendix on zorn's lemma and it's almost all you need lol

[vital bane]

that's common in math books though

[dim pendant]

who reads 70 pages on group theory before doing an exercise

[dim pendant]

true but at least section them out in the exercises 😭

[vital bane]

Oh nevermind yeah I see the issue

[vital bane]

Tbh every theorem and lemma is an exercise

[naive lava]

lang would probably be perfect if he actually explained stuff

[vital bane]

[vital bane]

Rudin moment

[dim pendant]

cough cough, Rudin

[vital bane]

Lmao

[naive lava]

since I've started to read other math books

I've seen how awful rudin is

It's still what I'd read

[vital bane]

bro has opened his eyes

[naive lava]

but yk

[vital bane]

tbh Rudin is good as a 2nd read

and as like an exercise books/reference book

[dim pendant]

"Hey guys, check out my analysis proof"
"Cool, how did you arrive at this?"
"I did the proof on my own, made it presentable, and then removed all of the important steps"

[naive lava]

on a subject you don't want to learn but wanna know

It's cool

which is almost all forms of analysis and algebra for me

[dim pendant]

Honestly I don't like Rudin at all

not good enough for a first pass, and the second half is generally thought to be garbage

[naive lava]

js read tu for diff forms tbh

[dim pendant]

but I love that he does topology before he works on limits and whatnot

[naive lava]

"topology"

[dim pendant]

Real analysis --> Differential forms in algebraic topology

[naive lava]

no no she(?) has a book on just manifolds

[dim pendant]

m*tric topology

[naive lava]

that starts out with R^n stuff

[dim pendant]

Ah okay, Tu has a book with the title I mentioned so I associated what you said with that book haha

[naive lava]

isn't that bott and tu

[dim pendant]

Yeah but that's still Tu there

Oh I see, I confused authorship with Tu's book "Differential geometry" or whatever

which is solely Tu

[naive lava]

uhh

that's actually a riemannian geo/bundle book

there is one more

[dim pendant]

... Can we all agree that Tu does too much geometry

[naive lava]

tu doesn't do enough geometry tbh

[dim pendant]

haha

all right great chatting but I got some homework to do and I'm running out of time

[naive lava]

good luck!

[cunning elk]

my real anal class didn’t even use a textbook for god knows why

and failed to cover everything that was supposed to be in the syllabus

have been meaning to go back and do the exercises in Pugh to brush up on my knowledge

[indigo notch]

What's a good book on linear regression?

[naive lava]

It's a pretty short topic, there probably won't many many books that are dedicated to it

[dim pendant]

YouTube might be the best book

[dim pendant]

I'm finished 💀 chapter was super short but I wait until the last minute so XD

[rigid trail]

bro censoring metric is crazy

😭

a lot of ppl here do 💀

[cunning elk]

m*tric sp*ces

[rigid trail]

i love metric spaces

[cunning elk]

we spent NINE weeks out of 15 on that shit

[rigid trail]

💜

[cunning elk]

and failed to actually cover differentiation and integration which were supposed to be on the syllabus

[rigid trail]

isnt a first course real analysis usually on metric topology though

whats wrong with talking about it a lot 😔

[cunning elk]

if we were doing rudin we wouldn’t have gotten past chapter 2

[rigid trail]

my course did not talk about differentiation at all, only defined it as a limit and left it at that

and we had 1-2 weeks on riemann/darboux integration

more like 1 week

[cunning elk]

we didn’t even get to that 😭

[rigid trail]

and then review for exams

so 1 week lol

[vital bane]

No Rolle's Theorem or Mean Value Theorem?

[rigid trail]

mvt proved during week of riemann integration

[cunning elk]

besides some basic exposition on sequences and series of funcs (only talked about pointwise vs uniform convergence 😭)

[rigid trail]

rolles theorem a corollary

[cunning elk]

a corROLLEary*

😁

[rigid trail]

shutupshutupshutupshutupshutupshutupshutupshutupshutupshutup

[cunning elk]

😭😭😭

[rigid trail]

💀

oh wait i remember now

one week on power series, one week on riemann integration

i kinda lumped them into one

[clear bobcat]

Hi I want a recommedation on projective geometry

[naive lava]

wait... ur profs don't js skip differentiation as an excersize on ur real anal class???

[cunning elk]

it was totally disorganized

[naive lava]

not really, it's a grad book

[cunning elk]

although I guess it did get mentioned offhand in recitation and there was a problem on it on the final

[naive lava]

that's kinda all you need in ug real analysis tho

[cunning elk]

hm really

[rigid trail]

it didnt get mentioned at all in any lecture in my course 💀

[cunning elk]

the class was unstructured to the point of being worse than useless at times

[naive lava]

if uniform conv. then everything you ever want happens(including that girl marrying you)

[rigid trail]

actually
prof didnt even define it until we were proving ftoc

[naive lava]

the greatest theorem of real anal

[rigid trail]

then he just wrote out defn while proving it

[cunning elk]

if compact*

[rigid trail]

like in the middle of proof

💀

[cunning elk]

and apparently the second semester class which I promptly switched out of for intro algebra

[naive lava]

rudin type shi

[cunning elk]

covered

normed vector spaces???

Fourier analysis

[rigid trail]

me when i discuss ftoc without having defined derivative

🗿

[cunning elk]

multivariate functions (to what extent i do not know)

[naive lava]

these are more FA

[naive lava]

definition of 4A

[cunning elk]

no idea I switched to algebra after lecture 1

😭

[vital bane]

Literally this (including you getting a Fields medal)

[rigid trail]

what are you studying

if you are math major, bruh 💀

[cunning elk]

wdym by that

[vital bane]

He's studying infinite dimensional algebraic topology

[cunning elk]

appmath whatever the hell thats supposed to mean

[rigid trail]

oh

[cunning elk]

I’ll take the second semester class my last semester

[naive lava]

[rigid trail]

yeah applied mathers can do whatever they want

math but easy mode fr

[naive lava]

wait why does that sound like absoulute fire tho

[vital bane]

ikr

[cunning elk]

math major stats traumatized me

[vital bane]

infinite dimensional holes

[naive lava]

suuure

[cunning elk]

homeworks were “prove all the stuff you took for granted in AP stats in excruciating detail”

[rigid trail]

for undergrad at least

idk anything about grad level

[vital bane]

Jordan Curve theorem

[cunning elk]

wilks’ theorem 💀

[vital bane]

John Wilks Booth?

💀

[cunning elk]

oh the single worst one I remember

[vital bane]

https://en.wikipedia.org/wiki/Wilks'_theorem

[rigid trail]

applied math having to prove things 💀

[vital bane]

I see

[cunning elk]

prove that the linear regression correlation coefficient was a t_(n-2) dist or smth

😭

[vital bane]

Also why is a full on conversation going on in #book-recommendations ?

[rigid trail]

bc yes

[vital bane]

shouldn't you guys go to #360643390594875392?

You can return it

[rigid trail]

just save it til you get that level

[cunning elk]

oh we amath students take a lot of the same classes that pure majors take

[vital bane]

or resell it (at a higher price)

[cunning elk]

our core requirements are slightly different is all

amath has prob/stats, intro analysis, numerical methods for core reqs

[naive lava]

check out the last problem in baez's book

[cunning elk]

pure I think has 2 semesters each of analysis and algebra for core reqs

but me when the “applied” classes are not in fact applied

[naive lava]

me when to apply something you have to know it

[cunning elk]

some of the course names are hilarious

“””””applied””””” combinatorics (nothing about it was applied, it’s just standard introductory combo)

“theory of numbers” (imagine calling the fire department the “department of fire”)

[vital bane]

Theory of fire

[cunning elk]

bag of body

[rigid trail]

cena of john

[dim pendant]

It's good if you're okay with dense, rigorous mathematics

I think it's a fine introduction for an undergraduate who has done a number of practice proofs outside of set theory, doesn't have to be a lot but yeah

[normal crystal]

Judson is free

[gloomy furnace]

Hello guys do you have any recommendation on books regarding the history of mathematics?

[gloomy furnace]

thanks

[balmy garden]

Does anybody know of a friendly but mature book on the elementary concepts of physics? something that makes you feel like you're really analyzing the fabric of reality rather than just doing calculus exercises

e.g., the examination of concepts like symmetries & energy, but nothing too subjective/philosophical

[normal crystal]

you actually prefer epub
btw this is the current site even though it's not the top search hit
https://judsonbooks.org/aata/

you are definitely not
but if you're reading on a tiny screen I understand

[normal crystal]

Conceptual Physics books are usually algebra based, like Hewitt
maybe you mean something like the Susskind series

no PC or laptop?
I could never do textbook reading limited to a phone
I salute your efforts🫡

[stable pike]

Hello I completed my undergraduate 4 years ago and now I am interested to relearn the maths can anyone recommend some nice books

[near jewel]

What is your goal? Simply refresh knowledge of math? Or deepen a specific field after refreshing?

[analog wadi]

can someone send me a solution manual for modern engineering mathematics fifth edition that is written by Glyn James?

[graceful moon]

I feel like given the price of them an iPad is just more worth your money

Or some other tablet, you can still write and annotate stuff on it but you can also do all the other things you would usually do on a tablet. IIRC remarkable is like £500 and you can easily pick up an iPad for pretty similar money

[orchid bridge]

anyone have any easy recommendations for a resource to learn lean programming? This is the textbook my professor told us to use: https://avigad.github.io/lamr/. Chapter 3 goes into lean programming immediately but i have very limited experience with coding and no experience with functional programming so im finding it really rough

[vital bane]

@rain hound might know about this

[rain hound]

Some suggestions you could go before diving into Lean.

• Lean is essentially a haskell clone in many ways so some exposure to Haskell isn't a bad idea. Learn You a Haskell is pretty accessible. https://learnyouahaskell.com/ You can just work through this until you feel more comfy with functional programming.
• The natural numbers game is a nice way to get some hands on experience with Lean https://adam.math.hhu.de/

For learning the language after that. Honestly, the Lean docs are pretty good imo. They're quite happy to learn from. Check out some of Lean's suggestions here https://leanprover-community.github.io/learn.html . Every resource I've looked at here thus far I've been quite happy with.

[orchid bridge]

ah okay thanks for the suggestions. Asked a senior the same question and he told me to try learning haskell first too, will look into that

[rain hound]

Some of them are good. E.g. Godsil, Royle Algebraic Graph Theory and Laaksonen Guide to Competitive Programming

oh my Judson has served in the trenches. I'm peeking at PreTeXt and it's basically like writing your book in html straight up omg.

It's a little better than that but, not much better

[cursive rivet]

software foundations by pierce et al https://softwarefoundations.cis.upenn.edu/, is in coq and not lean, but other than the syntax (which are quite similar) and some specific lean vs coq idioms (lean is more functional, coq has much better automation), I think it's a really good resource to learn from (if nothing else, for the explanations of some of the logical concepts, the really good exercises, and trying to do those proofs it gives in lean)

[rain hound]

It’s a good sequence of books but if you want to learn Lean you’re a lot better off just using one of the lean resources.

Pierce’s books aren’t a casual commitment. You follow along them by learning rocq and working through the book in rocq.

[cursive rivet]

I personally disagree, having had to learn Lean for a research assistant job a few months ago, but I did come at it with more programming background it seems

I found getting used to proof assistants and how I had to prove things to a computer were the hard part, and the transition between (rather unidiomatic) lean and rocq (minus automation) was essentially nothing

[balmy garden]

hmm, let me read a preview of some of them

@normal crystal , have you read any of the books from the Susskind series?

I'm interested in the classical mechanics book from it, so, if you've read it, how would you describe it? The preview I'm looking at doesn't really encompass the nature of it too well

[remote sparrow]

a lot of people buy e-ink tablets because they have fewer features than an ipad. also, e-ink displays don't strain eyes like ipads do. some mimic the feeling of writing on paper pretty well.

[late sundial]

Y’all got any contour integration book suggestions?

[remote sparrow]

in what context

multivariable calculus or complex analysis

[late sundial]

Complex

[dim pendant]

Are there actually books on complex variables that only care about contour integration

If you're looking for intuition, I suppose Needham's "Visual Complex Analysis" should be golden

[graceful moon]

I mean that seems silly to me but more power to you I guess

The screens are nice on them though I will say that, they are easy on the eyes

[rain hound]

For someone with ADHD it's actually a really great feature for staying focused, on task and hence productive. For a similar reason I prefer GNOME over KDE, precisely because it makes configuration a lot more difficult, so I'll just be productive instead of tinkering with my system all the time.

[north summit]

Is Functional Analysis, Calculus of Variations and Optimal Control by Francis Clarke good?

[full cairn]

getting distracted by config files is high-level ADHD linux must be a nightmare for you

[graceful moon]

Yeah thats fair, I have adhd too but I find just about a million things more distracting usually. In all honesty Ive never really used my ipad for anything other than writing

[full cairn]

e-ink displays are pretty nice to read though, I assume you can turn off the backlight like on a kindle, so that it's basically like reading paper?

[fervent obsidian]

Hi any recomendations about an introduction about foliations in geometry algebraic :¿

[cyan totem]

can confirm when I was using linux on a vm I spent like 3h configuring my terminal

[full cairn]

same, I installed arch linux a while back, and I spent 15 min on the actual installation, then 3 days configuring stuff

[balmy elm]

some linux distros include open source math texbooks just sayin

[rain hound]

I used to use neovim as an editor and it was soooooo bad oh my god.

I’ve managed the ADHD on linux by mostly sticking to distros and software that just work. Atm on Debian. Staying away from Arch.

[dim pendant]

Real

[misty galleon]

Hello I am looking for a nice Real Analysis + Complex Analysis textbook. Its not required that it be both, at the very least I'd take a very nice Real Analysis Textbook if it is that much better. I like visuals if possible, not a big fan of those novel-type texts that are just words. I know thats kind of how more advanced math is but if theres a nice one maybe even with color id be interested. Also intuitive explanations + proving everything it states

[molten gulch]

We've fallen back to arch and the only reason we haven't been obsessing over our book library or customizing the hell out of Arch is....school

[dim pendant]

I think that textbooks teaching real and complex analysis together are rare enough. Asking for pictures, too, doesn't leave much of anything to recommend for you.

"Visual Complex Analysis" is good for complex analysis. Idk what to use for real analysis but I'd suggest any popular book, for example Abbott or Tao. They're popular for a reason.

[misty galleon]

Okay thank you!

Does it matter which I start with?

Complex vs Real?

@dim pendant

[dim pendant]

Real analysis is generally considered better to begin with since complex analysis is, to an extent, developed in analogy to it. Also, real analysis is often a first rigorous math course a student takes, so complex analysis may be less friendly. But you should simply start with whatever interests you more, and move between your options as you come across boundaries.

[misty galleon]

okay thanks!

[misty galleon]

For the Tao books, how many parts are there?

I see part 1 and 2 are there any more?

[dim pendant]

I believe just two. And part 2 is a course in analysis in R^n so you can forget about it until you decide it's time to prepare for differential geometry or topology.

[misty galleon]

So a regular university class in real analysis would just be part 1?

[dim pendant]

Yeah, though his book has extra material. Usually analysis starts with the real numbers, not the naturals, or functions, or sets.

Do the whole thing though if you haven't done any math beyond calculus

[misty galleon]

are there exercises in it?

[misty galleon]

I plan on it

im a big fan of exercises

does it have them or even like a separate book for exercises?

[dim pendant]

If you can write proofs and are familiar with sets and functions of sets, you can safely skip to chapter 4

I believe it has exercises

[misty galleon]

cant : (

okay

[dim pendant]

No problem. If you struggle to follow the logic of the book when the proofs start, make sure to go through chapter 1 of Schramm's book "An Introduction to Real Analysis"

Or really any content on proofs. There's stuff on YouTube and all over math books

[misty galleon]

okay

[dim pendant]

There is none

There are just like three or four super popular books

One of many, but I guess to meet in the middle, sure it is

In generality, one should acquire Abbott and Tao, and move between them as desired. And there are some other notable mentions, such as Rudin (for structure, not learning on a first pass), Aman and Escher, Zorich (for students who want applications here and there), and more.

[heady ember]

How is Tao minimalist? Doesn't he yap a lot?

[dim pendant]

I find that he develops new ideas in excruciating detail

In the good sense, though

[worthy kindle]

then what is it minimal in ?

lol

[dim pendant]

"this book feels.. local"

[dim pendant]

Some areas of math are actually associated to colors in my head

For example, differential geometry and ODEs are blue, and complex analysis is yellow

[livid lintel]

Synesthesia?

[dim pendant]

Nah I imagine it's probably associations I've made between books I owned or studied

[normal crystal]

or they made it up rn
ya never know

[timber mesa]

huh that's interesting

[last cipher]

is there necessarily anything bad about using old resources from say the late 1960s

[timber mesa]

I don't think there's anything necessarily bad about that

you just gotta keep that in mind while reading

sometimes notation evolves, perspectives change as new tools are introduced later in the subject and as society itself changes

[last cipher]

I'm using evar nering's linear algebra 1st ed. for a theoretical treatment in the subject

[last cipher]

true

[timber mesa]

for linear algebra specifically I think it's surprising that many undergrad courses don't ever give a treatment of the SVD

[last cipher]

SVD?

[timber mesa]

given that's it maybe the main matrix decomposition used in numerical methods nowadays

singular value decomposition

it's also used in applied statistics, in principal component analysis

so stuff like that can sometimes shape what's important to the author of a textbook

and what's left out

more recent LA books are more likely to have some section or chapter about the SVD I guess

iirc Strang also very strongly advocated for college LA courses to see more matrix decompositions

[last cipher]

hmmm I see

But I should be good with the book im using right

If you'd like i could send you some of the photos of the content in it

[timber mesa]

yeah it's hard to find a bad book in linear algebra lol

I'll look it up and maybe skim the table of contents

dw

[last cipher]

okay

Full title of the book is "Linear Algebra and Matrix Theory" by Evar D Nering

[timber mesa]

got ahold of a copy, seems like a good selection of topics and it's well written

I'd take it over even Hoffman-Kunze which is from around the same time period lol

[last cipher]

Yeahhh

I got it for $20 (with shipping ofc) from thriftbooks

I honestly say it explains topics better than most modern books today

I wish textbooks were more like this though. Small and compact, loads of information

[timber mesa]

yeah I also like that kind of book

nice find

[remote sparrow]

20 is cheap in the states

[upper lynx]

does anyone knows a good textbook with exercises for geometry? (affine, euclidean, hermitian spaces, projective, bilinear and quadratic form)?

[remote sparrow]

for lower-division courses, like calculus, the books often come with online homework systems, which are pretty convenient for professors

[heady ember]

Idk if these online homework systems include automarkers, but automarkers suck balls in my experience.

[remote sparrow]

they often automatically grade work yeah

they also have buttons that notify the professor to review an answer manually

[native cradle]

is it just me or is artin not great for algebra

feels too terse

[heady ember]

Artin is too terse? That's the first time I've heard such a comment

If you meant it in the sense that Artin is too hard,

There are some books that are more introductory than these, such as "Gallian", "Pinter", "Fraleigh", etc. Honestly I feel like if you're struggling with D&F and Artin... you might not be ready for algebra yet, better to revisit foundations or smth.

[native cradle]

Like I'm used to more examples

I think that's what I meant

idk

I liked axler's style

maybe I'm going too fast

[dim pendant]

My issues with those algebra books is that they do way too much.. Like if you pick a random university in the US and you look at its undergraduate algebra class, it will basically be 40% groups, 50% ring analogy from groups, and 10% polynomial rings or linear algebra.

But then when someone asks to self study algebra we give them D&F which is enough actual material in algebra for someone going to specialize in group theory or AG or ANT

My favorite intro texts are Jacobson (first four chapters) and Herstein's "Topics in Algebra" since you don't feel like you're not doing enough

[graceful moon]

Is that an issue? I don’t think it’s reasonable for anyone to expect you to finish dummit and Foote in a semester

A significant number of textbooks are unreadable to finish in a semester or two, I don’t see that as a bad thing

[dim pendant]

I get the impression that most people asking for undergrad books are intending to read the entire thing

[graceful moon]

I again don’t see the issue here

You can read all of D&F, it just likely contains a superset of the course material

And you probably should know it all at some point if you plan to go down an algebra route

But you could very easily, depending on how many credits your course are, take 2-4 semesters to get through all of D&F, it’s a big book. I don’t see why that’s a problem though

[scarlet hollow]

can i have a reccoomendation for a combinatorics textbook and a number theory textbook

that i can get through by end of summer

[tender river]

Bona intro to enumerative and analytic combinatorics

[rain hound]

there’s a pretty significant number of books out there which have enough material to span 2 courses. Just how it is. Not everything is covered in one course and that’s ok. It can be a two parter.

[heady ember]

Ok now I feel better about having spent 2023-now on FIS and still not finishing it yet

:copium:

[rain hound]

I felt that it suffered from a typical issue of many books from “prestigious top ranked institutions”. It forgets what it was like to not know the subject and teaches with a lot of gaps and expects the student to just be brilliant and materialize the gaps out of nowhere. It’s flat and totally unmotivated. It’s supposed to be “obvious”.

[rain hound]

I liked Judson’s abstract algebra book (like Axler is freely available on his website). It’s an accessible undergrad book. Of course, that means you’ll have to relearn algebra again in grad school, but that’s probably a good idea anyway.

[last cipher]

unless you go to a thrift store

I have Stewart's Calculus

First edition

😎

Got it for 10 bucks

And tbh 20 for a book is fairly cheap because most books go on sale for $80-$120 CAD

[hasty eagle]

whyhello

[last cipher]

ok latex

[graceful moon]

Yeah I mean $20 is very cheap I don’t know how you could reasonably get a book for much less, aside from random charity shop finds

[rain hound]

used paperbacks can get cheaper

[last cipher]

even springer is so expensive 😔

[native cradle]

I have artin, jusdon and aluffi

currently using artin

[native cradle]

I feel axler doesn't suffer from that

[rain hound]

I agree

judson for undergrad + aluffi for grad is a pretty optimal combo imo

[native cradle]

hmm

[vernal tinsel]

Any book rec for modular forms applications in physics?

[native cradle]

thanks

[wicked fractal]

https://arxiv.org/abs/1511.04265

Peak read btw

[warm fiber]

Any thoughts on the book of proof, would you say there are any prerequisites for reading it

[floral lantern]

my problem with judson is that it doesn't have enough concrete problems "working with groups"

most of the problems in the book are trivial computation bash or abstract theory problems without concrete, nontrivial problems

[vernal tinsel]

Thanks

[dim pendant]

If you've already obtained it, simply try it out and see where it goes. Don't get bogged down by prerequisites until they actually hinder you

[vital bane]

Book for more concrete problems:

You are welcome

no need to thank me

[full cairn]

This book is also great if you're a civil engineer and want to know more about concrete

(it says a foundation for computer science, but that's just a misprint, it's supposed to say a foundation for buildings)

[warm fiber]

I haven't but I'm thinking of getting it or using the free pdf

[sage python]

I mean, buildings are relevant in computer science

https://en.m.wikipedia.org/wiki/Building_(mathematics)

[vital bane]

Jacques Tits mentioned

I know him from the Tits group

[floral lantern]

You are not the ohio alpha bro

[trail hemlock]

you called

[dim pendant]

If you can "acquire" a "free PDF copy" of it, i say go ahead and jump in

[molten gulch]

Hammack's book of proof is legally free btw

[dim pendant]

I believe it has to do with the tools they've picked up. For example, in your very first mechanics class you're probably using only single variable calculus, and then as you develop vector calculus, linear algebra and differential equations, you're better prepared to study things properly. Just my two cents.

[graceful moon]

You essentially don’t know enough maths to do physics until you’ve done 2 years of university level maths

I mean you could, but you can do a lot of labs and other classes to build physics intuition and problem solving

I started uni doing a degree in mathematical physics and we essentially did far more maths heavy courses to speed run that gap, we were about a year ahead of the normal physics track mathematically. It’s a good degree but just a different approach (though the courses were hellish, the genuine worst 2 years of my life)

[dim pendant]

What does a mathematical physics degree look like

In other words, what kind of classes are you taking

[cunning elk]

mathematical physics
so just physics?

seems like a bit of a silly name, the math is a huge part of higher level physics

[graceful moon]

We took all of the required maths courses, and essentially, at least for the period I did the degree, the same classes as the normal physics degree but like a year earlier (by this I mean we covered the same/similar content in a different class, they werent litterally the same). So like in my second semester I was learning about PDEs, greens functions, tensor calculus etc in my introduction to fields and waves class. My introduction to dynamics course was essetially just a harder version of the vector calculus and dynamics course the normal physics students take etc

I think the final 2 years of the degree are where it differs a lot more, but yeah in general they just take the harder versions / second courses on a topic because theyve all taken more maths courses

[cunning elk]

I wish i had more schedule space to take phys classes beyond the intro level 😔

(amath + piano double major, would’ve gone for a phys minor if I had the space)

[graceful moon]

Meh, its a degree where you dont do any experiments and your general relativity course is taught by the school of maths. Its essentially the same as the maths and physics (double major if youre American) so the name makes an ammount of sense

[normal crystal]

should physics be taught first year of HS
or junior year of college
YES🤡

[dim pendant]

I have the opposite opinion. Biology and chemistry should be taught every year. It's what politicians lie to people about, so the more of us who have a basic understanding of these disciplines, the better.

[normal crystal]

dw, neither of those options will happen

[dim pendant]

I chose a year of year of Chem and phys and two years of bio

A year of college bio and college chem so that they would be done and over when I got to uni lol

I'm sure that would change if you needed to study ochem

[graceful moon]

You may be the first person around to say Ochem might be what makes someone like chemistry

[dim pendant]

It feels like real analysis. A bunch of new concepts spat into your face and then you use your brain to learn all sorts of fascinating things

[dim pendant]

A combination of ochem, biochem, and Nile Red is what convinced me that Chem was based

I think everything starts out that way but over time you convert some memory into intuition

In science you get to play with things but in math you just do the exercises

[willow merlin]

does there exist a book that proves that $e = \lim_{n \to \infty} \left(1+\frac{1}{n}\right)^n$

[hasty eagle]

938c2cc0dcc05f2b68c4287040cfcf71

[rigid trail]

yes

[willow merlin]

can u name it please

[rigid trail]

no

i am unable to name it

you need to tell me your definition of e

[cunning elk]

PLENTY of such sources

this is one of the most classic results in all of math

[willow merlin]

like what books

[jovial mason]

[cunning elk]

literally just google "limit expression for e"???

[willow merlin]

that's what I am struggling, maybe b^x where b is nonzero and the derivative of b^x is b^x

[rigid trail]

the proof is diffenent depending on what you define e you start with...

[rigid trail]

okay

[willow merlin]

the proof of it I mean

[cunning elk]

and you'll find proofs of it more likely than not

[willow merlin]

I already tried but easiest one I found is using binomial theorem i guess

also, there must a simpler one right?

[rigid trail]

i think that's an unusual place to "start"

[willow merlin]

what other definition of e comes to mind?

[rigid trail]

you usually start with series expansion of e^x

then that implies (e^x)' = e^x

so if you "start" with (e^x)' = e^x you can probably show that e^x = series expansion

then from that you can prove limit

[willow merlin]

what definition are you using? the taylor expansion of e^x isn't taylor expansion an approximation or no?

[willow merlin]

how is it implied?

[rigid trail]

the infinite series

[rigid trail]

termwise differentiation

and change of indexing

you can see that differentiation doesnt affect

[willow merlin]

you are differentiating a taylor series,if I am understanding correctly?

[cunning elk]

https://www2.math.uconn.edu/~hurley/math116/section4_docs/Handouts/elimit.pdf

[rigid trail]

Yeah

you can show that differentiating the taylor series gives the same taylor series

[merry sphinx]

rudin, from the dfn of e as the sum of 1/n!

[rigid trail]

yeah with the taylor series then you have e = e^1 = sum of 1/n!

[merry sphinx]

in chapter 2

[rigid trail]

then the rest is in rudin and i think it's just binomial expansion

so suppose (e^x)' = e^x => arrive at taylor series of e^x => take e^1, 1/n! sum => binomial expansion in rudin

[graceful moon]

I mean I enjoyed chemistry too, I liked organic chemistry but I’d just be amazed if that’s what turned round a chemistry hater haha, it’s just kinda hard

[dim pendant]

True lol

[graceful moon]

It ended up being the only class I ever found hard in highschool, I felt the jump between the previous and final years chemistry was kinda insane

Though for Covid reasons I did have to self study is so that is potentially a compounding factor there

[dim pendant]

I had the opposite experience lmao during covid I took general Chem and my school thought everyone was stupid so all of the homework and notes were made available until the exam, so I just did math during lecture and did the homework with notes over and over until it clicked before the exam

Ended up with an A, with about 30 minutes of study per unit lol

But that's general chemistry for you

[naive lava]

there's a huge diff

math phy utilizes new types of math to explain current physics

other physicist don't really need that high level of math

like you won't find a particle physicist studying connections on fiber bundles where it's common info in math phy

[round pelican]

Is Derek Goldrei’s Propositional and Predicate Calculus: A Model of Argument a good first book to self study mathematical logic? For those who have read it what did you think of the book? Thank you!

[dim pendant]

Lol

Smarter is a wild statement but for comedic purposes I'll let it be

[naive lava]

not likely

I know solid state ppl that are much smarter than everyone in my dep

[last cipher]

Thoughts on

Elementary Analysis by Kenneth Ross?

Looking for an introductory analysis book

[rigid trail]

That's one of the books my course uses

It is okay

Some of it is very clear and good, but other parts are ehhh

I think abbott and rudin are better overall, abbott for introduction and rudin for more thorough

[last cipher]

Hmm okay..

Might just get ross' elem. analysis

[south scarab]

calculus textbook that mainly dives into proofs? much appreciated if you reply with ping

[remote sparrow]

spivak, apostol, kitchen

[south scarab]

which is most rigor?

also thank you

[remote sparrow]

they're all comparable

[vital bane]

The difference between those books is not "less rigorous" vs "more rigorous" the former books are the very basics of physics while the latter are more detailed and go further than the basics

so the former is a prerequsitie to the latter

[vital bane]

This is not really true, you can do perfectly fine physics with just elementary algebra and geometry (though calculus opens up a whole wide world but still)

Physics \neq math, or maybe you just have a narrow percetion of what "physics" is

[rigid trail]

Are you asking for analysis

[vital bane]

Yea knowing how to prove every integral domain has characteristic 0 or prime, or knowing how to prove the inverse function theorem will get you nowhere in physics because physics concerns itself with modeling the universe accurately

[floral lantern]

hey the skills you learn doing this are helpful (for some)

[vital bane]

The skills required for doing pure math and for doing physics are largely different

I mean of course getting a math degree before studying physics will help but it's not at all required

[graceful moon]

I’m aware, I did 6 years of highschool physics like that, but that wasn’t the question

The spirit of the question was very clearly why do you do a basic introduction to QM or thermo or whatever then just do it all again. My point is that until you’ve done about 2 years of university level maths is that you can’t do anything more advanced than simple particle in a box or god given formula plug and chug stuff. If you want to actually do quantum mechanics of electrodynamics or whatever you need to know more maths

[vital bane]

my point is basic QM and thermo are still very much physics and without the basics you can't move onto to more advanced stuff

Also

Same person?

[graceful moon]

I feel like you’re just ignoring the question that was originally asked

[vital bane]

He has literally gone off the deep end

[vital bane]

Yes

My statement was addressing to your statement

[graceful moon]

I did the first 2 years of a physics degree, I’m well aware of what they do. My comment was only intended in light of the question that was actually asked

[vital bane]

I guess you meant "physics" in the sense of the physics in Taylor and Griffith, I was just on guard because there generally seems to be a sentiment of "you need a lot of advanced rigorous math to study physics" when in reality all you need is MVC and lin alg

[vital bane]

you switched to a math major after 2 years of physics?

[vital bane]

@remote sparrow

[graceful moon]

That is exactly what I meant because it’s what was asked

[vital bane]

We aren't fighting

[graceful moon]

Yes, I wanted to switch immediately but I wasn’t allowed

[vital bane]

we are teaming up to beat you up

[vital bane]

Oh I see

[graceful moon]

For reasons that make sense to only my uni

[vital bane]

that sucks

But at least you're a math major now

[remote sparrow]

[graceful moon]

For another like 3 days

[remote sparrow]

did my article recommendations in #math-pedagogy help

#math-pedagogy message

[graceful moon]

I ended up changing topics for my essay unfortunately, decided to look at the role of examples in supporting the transition to tertiary maths

I actually have my oral exam for that class in a couple hours

Thank you for the guidance in any case though!

[remote sparrow]

[ripe cove]

I've a study group channel would anyone like to join?

[native cradle]

book suggestions for probability please

for an undegrad course in the same

[graceful moon]

I don’t have a recommendation but it’s probably worth mentioning if you mean elementary probability or like post measure theory probability

[native cradle]

a first course

[remote sparrow]

https://stat110.net

[native cradle]

Thanks

[naive lava]

IVT actually matters lol

since you do a lot of manifold stuff

[vital bane]

But its proof isn't relevant to physics

[naive lava]

meanwhile these books: https://www.amazon.com.be/-/en/Pierre-Deligne/dp/0821820125

[naive lava]

hmm

maaybe

but the proof for manifolds and supermanifolds go a bit differently

soo

maybe

[vital bane]

supermanifolds